%I #7 Sep 02 2022 18:06:56
%S 1,0,2,3,-4,30,954,6300,6432,424872,18273960,260682840,1754408424,
%T 47063118960,2314149100704,54798086299320,773632032345600,
%U 20746972036284480,1072205580591921600,36098491880448944640,816375193722964932480,25160238159364392336000
%N E.g.f. satisfies A(x)^(A(x)^2) = 1/(1 - x*A(x))^x.
%F a(n) = n! * Sum_{k=0..floor(n/2)} (n-3*k+1)^(k-1) * |Stirling1(n-k,k)|/(n-k)!.
%o (PARI) a(n) = n!*sum(k=0, n\2, (n-3*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
%Y Cf. A184949, A349559, A356786, A356787, A356884.
%Y Cf. A355767.
%K sign
%O 0,3
%A _Seiichi Manyama_, Sep 02 2022